Context. The origin and dynamical evolution of star clusters is an important topic in stellar astrophysics. Several models have been proposed to understand the formation of bound and unbound clusters and their evolution, and these can be tested by examining the kinematical and dynamical properties of clusters over a wide range of ages and masses. Aims. We use the Gaia-ESO Survey products to study four open clusters (IC 2602, IC 2391, IC 4665, and NGC 2547) that lie in the age range between 20 and 50 Myr. Methods. We employ the gravity index $gamma$ and the equivalent width of the lithium line at 6708 $AA$, together with effective temperature $rm{T_{eff}}$, and the metallicity of the stars in order to discard observed contaminant stars. Then, we derive the cluster radial velocity dispersions $sigma_c$, the total cluster mass $rm{M}_{tot}$, and the half mass radius $r_{hm}$. Using the $Gaia$-DR1 TGAS catalogue, we independently derive the intrinsic velocity dispersion of the clusters from the astrometric parameters of cluster members. Results. The intrinsic radial velocity dispersions derived by the spectroscopic data are larger than those derived from the TGAS data, possibly due to the different masses of the considered stars. Using $rm{M}_{tot}$ and $r_{hm}$ we derive the virial velocity dispersion $sigma_{vir}$ and we find that three out of four clusters are supervirial. This result is in agreement with the hypothesis that these clusters are dispersing, as predicted by the residual gas expulsion scenario. However, recent simulations show that the virial ratio of young star clusters may be overestimated if it is determined using the global velocity dispersion, since the clusters are not fully relaxed.
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